Hypervelocity ejection of material by impact spallation is considered a plausible mechanism for material exchange between two planetary bodies. We have modeled the spallation process during vertical impacts over a range of impact velocities from 6 to 21 km/s using both grid- and particle-based hydrocode models. The Tillotson equations of state, which are able to treat the nonlinear dependence of density on pressure and thermal pressure in the strongly shocked matter, were used to study the hydrodynamic and thermodynamic response after impacts. The effects of material strength and gravitational acceleration were not considered. A two-dimensional time-dependent pressure field within a 1.5-fold projectile radius from the impact point was investigated in cylindrical coordinates to address the generation of spalled material. A resolution test was also performed to reject ejected materials with peak pressures that were too low due to artificial viscosity. The relationship between ejection velocity veject and peak pressure Ppeak was also derived. Our approach shows that late stage acceleration in an ejecta curtain occurs due to the compressible nature of the ejecta, resulting in an ejection velocity that can be higher than the ideal maximum of the resultant particle velocity after passage of a shock wave. We also calculate the ejecta mass that can escape from a planet like Mars (i.e., veject higher than 5 km/s) that matches the petrographic constraints from Martian meteorites, and which occurs when Ppeak from 30-50 GPa. Although the mass of such ejecta is limited to from 0.1-1 percent of the projectile mass in vertical impacts, this is sufficient for spallation to have been a plausible mechanism for the ejection of Martian meteorites. Finally, we propose that impact spallation is a plausible mechanism for the generation of tektites.